Luca Sabatini

activity

20242026

most citedFixing two points in primitive solvable groups

2 citations · 3 across the 4 of their papers we have counts for

collaborators

5 papers

math.GR2026

Arithmetic properties of solubilizers

Luca Sabatini

Let $G$ be a finite group and $x \in G$ . In 2013, Hai-Reuven proved that the cardinality of the centralizer of $x$ divides the cardinality of the solubilizer of $x$ . Settling a con…

math.GR2026

Sylow synchronization in finite groups: the good case

Hong Yi Huang, Francesca Lisi, Aluna Rizzoli +1

Let $G$ be a finite solvable group such that, for any prime $p$ and any quotient $Q$ of $G$ , there are two Sylow $p$ -subgroups of $Q$ intersecting in $O_{p} (Q)$ . Then, for every fami…

math.GR2026

Diameter bounds for arbitrary finite groups and applications

Sean Eberhard, Elena Maini, Luca Sabatini +1

We prove a strong general-purpose bound for the diameter of a finite group depending only on the diameters of its composition factors and the maximal exponent of a normal abelian s…

math.GR2025★ 1 cited

Sylow subgroups for distinct primes and intersection of nilpotent subgroups

Francesca Lisi, Luca Sabatini

Let $G$ be a finite group and let $(P_{i})_{i = 1}^{n}$ be Sylow subgroups for distinct primes $p_{1}, \dots, p_{n}$ . We conjecture that there exists $x \in G$ such that $P_{i} \cap P_{i}^{x}$ is i…

math.GR2024★ 2 cited

Fixing two points in primitive solvable groups

Francesca Lisi, Luca Sabatini

Consider a finite primitive solvable group. We observe that a result of Y. Yang implies that there exist two points whose pointwise stabilizer has derived length at most $9$ . We sh…